Embedding Diagrams

The large ball will cause a deformation in the sheet's surface. A baseball
dropped onto the sheet will roll toward the bowling ball. Einstein theorized
that smaller masses travel toward larger masses not because they are
"attracted" by a mysterious force, but because the smaller objects
travel through space that is warped by the larger object. Physicists
illustrate this idea using embedding diagrams.

Contrary to appearances, an embedding diagram does not depict
the three-dimensional "space" of our everyday experience. Rather it shows how a 2D slice through familiar 3D space is curved downwards when embedded in flattened hyperspace. We cannot fully envision this hyperspace; it contains seven dimensions, including
one for time! Flattening it to 3D allows us to represent the curvature. Embedding diagrams can help us visualize the implications of Einstein's General Theory of Relativity.

The Flow of Spacetime

Another way of thinking of the curvature of spacetime was elegantly described by Hans von Baeyer. In a prize-winning essay he conceives of spacetime as an invisible stream flowing ever onward, bending in response to objects in it
s path, carrying everything in the universe along its twists and turns.

This is a basic postulate of the Theory of General Relativity. It states
that a uniform gravitational field (like that near the Earth) is equivalent
to a uniform acceleration.

What this means, in effect, is that a person cannot tell the difference between (a) standing on the Earth,
feeling the effects of gravity as a downward pull and (b) standing in a very smooth elevator
that is accelerating upwards at just the right rate of exactly 32 feet per second squared.
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In both cases, a person would feel the same downward pull of gravity.
Einstein asserted that these effects were actually the same. A far cry from Newton's view of gravity as a force acting at a distance!

Einstein's Special Theory of Relativity predicted that time does not flow at a fixed rate: moving clocks appear to tick more slowly relative to their stationary counterparts. But this effect only becomes really significant at very high velocities that app
roach the speed of light.

When "generalized" to include gravitation, the equations of relativity predict that gravity, or the curvature of spacetime by matter, not only stretches or shrinks distances (depending on their direction with respect to the gravitational field) but also w
ill appear to slow down
or "dilate" the flow of time.

In most circumstances in the universe, such time dilation is miniscule, but it can become very significant when spacetime is curved by a massive object such as a black hole. For example, an observer far from a black hole would observe time passing
extremely slowly for an astronaut falling through the hole's boundary. In fact, the distant observer would never see the hapless victim actually fall in. His or her time, as measured by the observer, would appear to stand still. The slowing of time near
a very simple black hole has been simulated on supercomputers at NCSA and visualized in a computer-generated animation.

Grappling With Relativity

In the decade after its publication in 1916, Einstein's Theory of General Relativity led to a burst of experimental activity in which many of its predictions were vindicated. These predictions were encapsulated in a series
of field equations that laid the foundation for all subsequent research into relativity and partly for modern cosmology as well.

The Math Behind Einstein's Vision

The mathematics behind the Einstein Field Equations not only presented a formidable challenge to solve, but also led to seemingly bizarre consequences, particularly those of black holes and gravitatio
nal waves. At the time they were postulated, both were dismissed by many experts as mathematical aberrations. It remains to be seen whether either truly exist.

Rest assured that the next section will further illuminate your grasp of relativity -- without math overload!